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Thought-Process to Discover Knowledge

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Modulus of product is product of modulus.



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Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2` what is the modulus of product `|z_1 xx z_2|`?

  • `|z_1| xx |z_2|`
  • `|z_1| xx |z_2|`
  • `|z_1| + |z_2| `

The answer is '`|z_1| xx |z_2|`'.

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2`, the modulus of product
`|z_1 xx z_2|`
`quad quad = |a_1a_2-b_1b_2 + i(b_1a_2+a_1b_2)|`
`quad quad = sqrt(a_1^2+b_1^2)sqrt(a_2^2+b_2^2)`
`quad quad = |z_1| xx |z_2|`

 •  Modulus of product is product of modulus.

Modulus of Product: For complex numbers `z_1, z_2 in CC`

`|z_1 xx z_2| = |z_1| xx |z_2|`

Solved Exercise Problem:

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2` what is the modulus of quotient `|z_1 -: z_2|`?

  • `|z_1| -: |z_2|`
  • `|z_1| -: |z_2|`
  • `|z_1| - |z_2| `

The answer is '`|z_1| -: |z_2|`'.

                            
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